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Publications Influence

RACKS AND LINKS IN CODIMENSION TWO

A rack, which is the algebraic distillation of two of the Reidemeister moves, is a set with a binary operation such that right multiplication is an automorphism. Any codimension two link has a… Expand

443 40

The braid-permutation group

- R. Fenn, Richárd Rimányi, C. Rourke
- Mathematics
- 1997

Abstract We consider the subgroup of the automorphism group of the free group generated by the braid group and the permutation group. This is proved to be the same as the subgroup of automorphisms of… Expand

154 16

A Geometric Approach to Homology Theory

- S. Buonchristiano, C. Rourke, B. Sanderson
- Mathematics
- 30 April 1976

1. Homotopy functors 2. Mock bundles 3. Coefficients 4. Geometric theories 5. Equivariant theories and operations 6. Sheaves 7. The geometry of CW complexes.

115 14

Trunks and classifying spaces

- R. Fenn, C. Rourke, B. Sanderson
- Mathematics, Computer Science
- Appl. Categorical Struct.
- 1 December 1995

Trunks are objects loosely analogous to categories. Like a category, a trunk has vertices and edges (analogous to objects and morphisms), but instead of composition (which can be regarded as given by… Expand

170 13

On Kirby's calculus of links

(Receiued in revised form 21 July 1978) 4 FRAMED OR labelled link in S3 is a finite collection L of embedded circles in S’, each one of which is labelled by an integer. In [3] and [7] Lickorish and… Expand

135 10

Ordering the braid groups

- R. Fenn, M. T. Greene, D. Rolfsen, C. Rourke, B. Wiest
- Mathematics
- 3 September 1998

We give an explicit geometric argument that Artin’s braid group Bn is rightorderable. The construction is elementary, natural, and leads to a new, effectively computable, canonical form for braids… Expand

93 7- PDF

The compression theorem I

- C. Rourke, B. Sanderson
- Mathematics
- 9 December 1997

This the first of a set of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie,… Expand

57 7- PDF

THE EXISTENCE OF COMBINATORIAL FORMULAE FOR CHARACTERISTIC CLASSES

Given a characteristic class on a locally ordered combinatorial manifold M there exists a cocycle which represents the class on M and is locally defined, i.e. its value on a E M depends only on the… Expand

24 6- PDF

The rack space

- R. Fenn, C. Rourke, B. Sanderson
- Mathematics
- 16 April 2003

The main result of this paper is a new classification theorem for links (smooth embeddings in codimension 2). The classifying space is the rack space and the classifying bundle is the first James… Expand

67 4- PDF

An Introduction to Species and the Rack Space

- R. Fenn, C. Rourke, B. Sanderson
- Mathematics
- 1993

Racks were introduced in [FR]. In this paper we define a natural category like object, called a species.* A particularly important species is associated with a rack. A species has a nerve, analogous… Expand

66 3

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